GCF of 9 and 12


The gcf of 9 and 12 is the largest positive integer that divides the numbers 9 and 12 without a remainder. Spelled out, it is the greatest common factor of 9 and 12. Here you can find the gcf of 9 and 12, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 9 and 12, but also that of three or more integers including nine and twelve for example. Keep reading to learn everything about the gcf (9,12) and the terms related to it.

What is the GCF of 9 and 12

If you just want to know what is the greatest common factor of 9 and 12, it is 3. Usually, this is written as

gcf(9,12) = 3

The gcf of 9 and 12 can be obtained like this:

  • The factors of 9 are 9, 3, 1.
  • The factors of 12 are 12, 6, 4, 3, 2, 1.
  • The common factors of 9 and 12 are 3, 1, intersecting the two sets above.
  • In the intersection factors of 9 ∩ factors of 12 the greatest element is 3.
  • Therefore, the greatest common factor of 9 and 12 is 3.

Taking the above into account you also know how to find all the common factors of 9 and 12, not just the greatest. In the next section we show you how to calculate the gcf of nine and twelve by means of two more methods.

How to find the GCF of 9 and 12

The greatest common factor of 9 and 12 can be computed by using the least common multiple aka lcm of 9 and 12. This is the easiest approach:

gcf (9,12) = $\frac{9 \times 12}{lcm(9,12)} = \frac{108}{36}$ = 3

Alternatively, the gcf of 9 and 12 can be found using the prime factorization of 9 and 12:

  • The prime factorization of 9 is: 3 x 3
  • The prime factorization of 12 is: 2 x 2 x 3
  • The prime factors and multiplicities 9 and 12 have in common are: 3
  • 3 is the gcf of 9 and 12
  • gcf(9,12) = 3

In any case, the easiest way to compute the gcf of two numbers like 9 and 12 is by using our calculator below. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 9,12. The calculation is conducted automatically.

The gcf is...
Frequently searched terms on our site also include:

Use of GCF of 9 and 12

What is the greatest common factor of 9 and 12 used for? Answer: It is helpful for reducing fractions like 9 / 12. Just divide the nominator as well as the denominator by the gcf (9,12) to reduce the fraction to lowest terms.

$\frac{9}{12} = \frac{\frac{9}{3}}{\frac{12}{3}} = \frac{3}{4}$.

Properties of GCF of 9 and 12

The most important properties of the gcf(9,12) are:

  • Commutative property: gcf(9,12) = gcf(12,9)
  • Associative property: gcf(9,12,n) = gcf(gcf(12,9),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.

To sum up, the gcf of 9 and 12 is 3. In common notation: gcf (9,12) = 3.

If you have been searching for gcf 9 and 12 or gcf 9 12 then you have come to the correct page, too. The same is the true if you typed gcf for 9 and 12 in your favorite search engine.

Note that you can find the greatest common factor of many integer pairs including nine / twelve by using the search form in the sidebar of this page.

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